I used to fly into Toronto and Montreal quite a bit and saw many fellow crewmembers dealing with this. Most of the time the problem was with DUIs, not a felony in the US but apparently in Canada they are, which disqualifies one from entering their country. I have no idea about driving across the border but if you fly in, you will be detained if you have a felony on your record and you will not be allowed in to Canada. Maybe they don't run every passport at the road checkpoints
Crew could get permission to enter but it involved going through some process with the Canadian government. Not sure if that is available to everybody, I'll let you figure that out.